Question

question 5
solve the equation $18 - |x - 4| = 10$.
(fill each blank with an integer where the smaller integer is on the first blank.)
$x = \square$ or $x = \square$

Explanation:

Step1: Isolate the absolute value term

$18 - |x-4| = 10 \implies -|x-4| = 10 - 18$
$\implies -|x-4| = -8 \implies |x-4| = 8$

Step2: Split into two linear equations

Case 1: $x - 4 = 8$
Case 2: $x - 4 = -8$

Step3: Solve each linear equation

Case1: $x = 8 + 4 = 10$
Case2: $x = -8 + 4 = -2$

Step4: Order solutions (smallest first)

Smaller value: $-2$, Larger value: $10$

Answer:

$x = -2$ or $x = 10$